Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-21T09:13:25.358Z Has data issue: false hasContentIssue false
  • English
  • Français

The shape of free jets of water under gravity

Published online by Cambridge University Press:  11 April 2006

E. O. Tuck
E. O. Tuck
Affiliation:
Applied Mathematics Department, University of Adelaide, South Australia 5001
Get access Rights & Permissions [Opens in a new window]

Abstract

A study is made of the form taken by a slender jet of water whose only boundary is a free surface. The only forces acting are inertial and gravitational. Attention is paid to the cross-flow velocity components and to the development of the shape of the cross-section of the jet as it progresses. It is established that a jet with initially elliptic cross-sections can remain elliptical, and the variation in the aspect ratio along the jet is determined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 4 , 25 August 1976 , pp. 625 - 640
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chandrasekhar, S. 1968 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Clarke, N. S. 1965 On two-dimensional inviscid flow in a waterfall. J. Fluid Mech 22, 359–369.Google Scholar
Conway, W. E. 1967 The two-dimensional vertical jet under gravity. J. Math. Anal. Appl 19, 282–290.Google Scholar
Friedrichs, K. O. 1948 Derivation of the shallow water theory. Comm. Pure Appl. Math 1, 81–88.Google Scholar
Keady, G. 1973 The jet from a horizontal slot at large Froude number. Proc. Camb. Phil. Soc 73, 515–529.Google Scholar
Keady, G. & Norbury, J. 1975 The jet from a horizontal slot under gravity. Proc. Roy. Soc. A 344, 471–487.Google Scholar
Keller, J. B. & Geer, J. 1973 Flows of thin streams with free boundaries. J. Fluid Mech 59, 417–432.Google Scholar
Keller, J. B., Rubinow, S. I. & Tu, Y. O. 1973 Spatial instability of a jet. Phys. Fluids, 16, 2052–2055.Google Scholar
Keller, J. B. & Wietz, M. L. 1957 A theory of thin jets. 9th Int. Cong. Appl. Mech. (Brussels), pp. 316–323.Google Scholar
Lamb, H. 1932 Hydrodynamics, 5th edn. Cambridge University Press.
Longuet-Higgins, M. S. 1972 A class of exact, time-dependent, free-surface flows. J. Fluid Mech 55, 529–543.Google Scholar
Rayleigh, Lord 1945 The Theory of Sound, vol. 2, 2nd edn republication. Dover.
Shapiro, A. 1953 The Dynamics and Thermodynamics of Compressible Fluid Flow, vol. 1. New York: Ronald.
Streeter, V. L. (ed.) 1961 Handbook of Fluid Dynamics. McGraw-Hill.
Taylor, G. I. 1960 Formation of thin flat sheets of water. Proc. Roy. Soc. A 259, 1–17.Google Scholar
Tuck, E. O. 1974 One-dimensional flows as slender-body problems, with applications to ships moving in channels. Proc. Workshop on Slender-Body Theory, Ann Arbor, June 1973. Univ. Michigan Rep. N.A.M.E. no. 164, pp. 27–35.
Tuck, E. O. 1975a Matching problems involving flow through small holes. Adv. Appl. Mech 15, 89–158.Google Scholar
Tuck, E. O. 1975b On air flow over free surfaces of stationary water. J. Austr. Math. Soc. B 19, 66–80.Google Scholar